Author and Astrophysicist

Entropy and Billy Pilgrim

The Second Law of Thermodynamics — entropy never decreases in a closed system — is among the more famous laws of physics. If you’re reading this blog, I’d be surprised if you’ve never heard of entropy before. You’ve probably also heard that entropy has something to do with disorder, and that the Second Law basically says that the universe tends toward disorder, but that’s not quite what the second law says — entropy isn’t really the same thing as disorder, though they’re related.

American planes, full of holes and wounded men and corpses took off backwards from an airfield in England. Over France, a few German fighter planes flew at them backwards, sucked bullets and shell fragments from some of the planes and crewmen. They did the same for wrecked American bombers on the ground, and those planes flew up backwards to join the formation.

The formation flew backwards over a German city that was in flames. The bombers opened their bomb bay doors, exerted a miraculous magnetism which shrunk the fires, gathered them into cylindrical steel containers, and lifted the containers into the bellies of the planes. The containers were stored neatly in racks. The Germans below had miraculous devices of their own, which were long steel tubes. They used them to suck more fragments from the crewmen and planes. But there were still a few wounded Americans, though, and some of the bombers were in bad repair. Over France, though, German fighters came up again, made everything and everybody as good as new.

When the bombers got back to their base, the steel cylinders were taken from the racks and shipped back to the United States of America, where factories were operating night and day, dismantling the cylinders, separating the dangerous contents into minerals. Touchingly, it was mainly women who did this work. The minerals were then shipped to specialists in remote areas. It was their business to put them into the ground, to hide them cleverly, so they would never hurt anybody ever again.

If you’ve read Slaughterhouse-Five, then you know that Billy Pilgrim has come unstuck in time, and he is witnessing the firebombing of Dresden backwards. But forget that for a moment and just look at the sequence of events described. Is this physically impossible? More specifically, does it directly violate any of the laws of physics that govern the behavior of the world at the level of the atoms and molecules involved?

As it turns out, the answer is no: at the atomic and subatomic level, the laws of physics are nearly perfectly reversible.1 Chemistry students know that any reaction that can go forwards can also go backwards, though it may not happen very often. There is, in theory, no law of physics that would be incontrovertibly violated by the “un-firebombing” of Dresden, as witnessed by Billy Pilgrim.

So why don’t we see this happening? Another quote, this time from Tolstoy:

Happy families are all alike; every unhappy family is unhappy in its own way.

Dresden, firebombed or not, is made of a million trillion trillion atoms, give or take a few zeroes. There are many, many ways to arrange and re-arrange those atoms — a fabulously huge number, so large it’s hard to get a grasp on how vast it is. And the overwhelming majority of that gigantic number of configurations lead to a total mess, rather than an intact Dresden. So just like Tolstoy’s families, there are many more ways for Dresden to be unhappy than happy. This is, fundamentally, why we don’t see bombed-out cities spontaneously reassemble: it’s not impossible, it’s just fabulously unlikely.

As it turns out, saying that there are more ways for Dresden to be in rubble than for Dresden to be intact is just another way of saying destroyed-Dresden has higher entropy than intact Dresden. This isn’t an approximation or simplification — this is exactly what entropy is. Entropy measures how many different ways a thing can be in a particular state. So when we say things tend towards states with higher entropy, what we’re saying is that stuff ends up in more likely states. And again, just like Tolstoy’s families, the most likely state for most things is what we usually think of as disorder — atoms strewn about every which way, as opposed to a very special and unique arrangement which we call “order.” So the Second Law of Thermodynamics doesn’t say that the universe tends toward disorder per se. The universe simply tends toward more likely stuff, and disorder is more likely than order, since there are (many, many) more ways to be disordered than ordered.

So it goes.

The exception is phenomena governed by the weak nuclear force, like certain kinds of radioactive decay. But that doesn’t play a role here — everything described by Vonnegut is governed by gravity and electromagnetism, and those are perfectly reversible at the subatomic level. [↵]